986.411
The respective 12 and 30 pentahedra OABAB of the rhombic
dodecahedron
and the triacontahedron may be symmetrically subdivided
into four right-angled tetrahedra
ABCO, the point C being surrounded by three right angles
ABC, BCO, and ACO. Right-
angle ACB is on the surface of the rhombic-hedra system
and forms the face of the
tetrahedron ABCO, while right angles BCO and ACO are
internal to the rhombic-hedra
system and from two of the three internal sides of the
tetrahedron ABCO. The rhombic
dodecahedron consists of 48 identical tetrahedral modules
designated ABCOd. The
triacontahedron consists of 120 (60 positive and 60
negative) identical tetrahedral modules
designated ABCOt, for which tetrahedron ABCOt we also
introduce the name T Quanta Module.

986.412
The primitive tetrahedron of volume 1 is subdivisible
into 24 A Quanta
Modules. The triacontahedron of exactly tetravolume
5, has the maximum-limit case of
identical tetrahedral subdivisibility__i.e., 120 subtetra.
Thus we may divide the 120
subtetra population of the symmetric triacontahedron
by the number 24, which is the
identical subtetra population of the primitive omnisymmetrical
tetrahedron: 120/24=5.
Ergo, volume of the A Quanta Module = volume of the
T Quanta Module.

(Footnote 5: C Quanta Modules and D Quanta Modules are added to the
A and B Quanta Modules to compose the regular tetrahedron as shown in
drawing B of Fig. 923.10.)

986.414
The vertical central-altitude line of the regular,
primitive, symmetrical
tetrahedron may be uniformly subdivided into four vertical
sections, each of which we may
speak of as quarter-prime-tetra altitude units-each
of which altitude division points
represent the convergence of the upper apexes of the
A, B, C, D, A', B', C', D', A", B",
C", D" . . . equivolume modules (as illustrated in Fig.
923.10B where__prior to the
discovery of the E "Einstein" Module__additional modules
were designated E through H,
and will henceforth be designated as successive ABCD,
A'B'C'D', A"B"C"D" . . .
groups). The vertical continuance of these unit-altitude
differentials produces an infinite
series of equivolume modules, which we identify in vertical
series continuance by groups
of four repetitive ABCD groups, as noted parenthetically
above. Their combined group-of-
four, externally protracted, altitude increase is always
equal to the total internal altitude of
the prime tetrahedron.

986.415
The rhombic triacontahedron has a tetravolume of 5,
wherefore each of its
120 identical, internal, asymmetric, component tetrahedra
ABCOt, the T Quanta Module,
has a tetravolume of 5/120 = 1/24 tetravolume__ergo,
the volume of the T Quanta
Module is identical to that of the A and B Quanta Modules.
The rhombic dodecahedron's
48 ABCOd asymmetric tetrahedra equal three of the rhombic
triacontahedron's 120
ABCOt , T Quanta Module asymmetric tetrahedra. The rhombic
triacontahedron's ABCOt
T Quanta Module tetrahedra are each 1/24 of the volume
of the primitive "regular"
tetrahedron__ergo, of identical volume to the A Quanta
Module. The A Mod, like the T
Mod, is structurally modeled with one of its four corners
omnisurrounded by three right
angles.

986.417 I find that it is important in exploratory effectiveness
to remember__as we
find an increasingly larger family of equivolume but
angularly differently conformed
quanta modules__that our initial exploration strategy
was predicated upon our
generalization of Avogadro's special-case (gaseous)
discovery of identical numbers of
molecules per unit volume for all the different chemical-element
gases when individually
considered or physically isolated, but only under identical
conditions of pressure and
heat. The fact that we have found a set of unit-volume,
all-tetrahedral modules__the
minimum-limit structural systems__from which may be aggregated
the whole hierarchy
of omnisymmetric, primitive, concentric polyhedra totally
occupying the spherically spun
and interspheric accommodation limits of closest-packable
nuclear domains, means that
we have not only incorporated all the min-max limit-case
conditions, but we have found
within them one unique volumetric unit common to all
their primitive conformational
uniqueness, and that the volumetric module was developed
by vectorial__i.e.,
energetic__polyhedral-system definitions.

986.418
None of the tetrahedral quanta modules are by themselves
allspace-filling,
but they are all groupable in units of three (two A's
and one B__which is called the Mite)
to fill allspace progressively and to combine these
units of three in nine different ways__all
of which account for the structurings of all but one
of the hierarchy of primitive,
omniconcentric, omnisymmetrical polyhedra. There is
one exception, the rhombic
triacontahedron of tetravolume 5__i.e., of 120 quanta
modules of the T class, which T
Quanta Modules as we have learned are of equivolume
to the A and B Modules.

986.419
The 120 T Quanta Modules of the rhombic triacontahedron
can be grouped
in two different ways to produce two different sets
of 60 tetrahedra each: the 60 BAAO
tetrahedra and the 60 BBAO tetrahedra. But rhombic triacontahedra
are not allspace-filling
polyhedra. (See Fig.
986.419.)